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Properties

Label 24.2.f
Level $24$
Weight $2$
Character orbit 24.f
Rep. character $\chi_{24}(11,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(24, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2 q - 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + 4 q^{12} + 8 q^{16} - 8 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} - 10 q^{25} + 10 q^{27} + 8 q^{33} + 16 q^{34} + 4 q^{36} - 20 q^{43} - 8 q^{48} + 14 q^{49} - 16 q^{51} + 4 q^{54} - 4 q^{57} - 16 q^{64} + 8 q^{66} + 28 q^{67} + 16 q^{72} + 4 q^{73} + 10 q^{75} - 8 q^{76} - 14 q^{81} - 32 q^{82} + 16 q^{88} + 16 q^{96} - 20 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.2.f.a 24.f 24.f $2$ $0.192$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)